I have recently gotten into speedrunning this game and I want to post a run, but the rules state that I must use a 'normal' version of the game and only list the one on itch. My school has banned itch for being a game site, and the only version I can practice on and play is the Coolmathgames version. Am I allowed to use the Coolmathgames version or no?

I just went ahead and tested the coolmathgames version, and it seems to be identical to the itch/steam version in terms of timing. As long as you make sure the timer is visible in the top right corner and adhere to the other general rules, then yeah, I'd say you're good to submit them! I'll make sure to change the rules to reflect this!